$ontext

   Test regression solver again a large simulated data set

$offtext

set i 'cases' /case1*case20000/;
set j 'parameters' /p0*p100/;
set j0(j) 'constant term' /p0/;
set j1(j) 'non-constant term' /p1*p100/;


parameter x(i,j) 'data, randomly generated; first column is constant term';
x(i,j0) = 1;
x(i,j1) = uniform(-100,100);

parameter p_sim(j) 'values of parameters to construct simulation';
p_sim(j) = ord(j);

parameter y(i) 'data, simulated';
y(i) = sum(j, p_sim(j)*x(i,j)) + normal(0,10);

variables
   p_est(j)  'parameters, to be estimated'
   sse       'sum of squared errors'
;
equation
   obj       'dummy objective'
   fit(i)    'equation we want to fit'
;

obj.. sse =n= 0;
fit(i).. y(i) =e= sum(j, p_est(j)*x(i,j));

$onecho > ls.opt
* increase default limits
maxn 30000
maxp 200
$offecho

option lp=ls;
model ols1 /obj,fit/;
ols1.optfile=1;
solve ols1 minimizing sse using lp;